Optimized multiple precision basic linear computation, especially matrix multiplication, is crucial for solving ill-conditioned problems. The recently proposed Ozaki scheme, which implements accurate matrix multiplication using existing optimized low precision matrix multiplication, is known to be useful for multiple precision as well. In this paper, we implement fixed precision multi-component-way matrix multiplication using Ozaki scheme and show that in some cases it is faster than existing optimized matrix multiplications. We also show that arbitrary precision matrix multiplication using Ozaki scheme is also faster than Strassen matrix multiplication up to a certain precision.
翻译:最佳的多精度基本线性计算,特别是矩阵乘法,对于解决条件不成熟的问题至关重要。 最近提议的奥崎计划(Ozaki program)使用现有优化的低精度矩阵乘法进行精确的矩阵乘法,也可用于多重精确度。在本文中,我们使用奥崎计划(Ozaki)实施固定的精度多元路矩阵乘法,并表明在某些情况下比现有优化的矩阵乘法更快。我们还表明,使用奥崎计划(Ozaki)的任意精确矩阵乘法也比Strassen 矩阵乘法更快,达到一定的精确度。